Please show all work and answer the following in Matlab code !!!For part c, clearly state the root with linear convergence so that part d may be executed. Please allow the codes to be copied directly into MatlabThis is a part of an ungraded test review so please help!! Given the polynomial function:\[ f(x) = 54x^6 + 45x^5 - 102x^4 - 69x^3 + 35x^2 + 16x - 4. \]### Tasks:**(b)** Apply Newton's Method to find all five roots within the interval with an accuracy of eight decimal places.**(c)** For each root, use the value obtained in part (b) to approximate its exact value \( r \). Define the error as \( e_i = |x_i - r| \), which represents the absolute error at step \( i \) in part (b). Plot the curve \( (e_i, e_{i+1}) \). Utilize a logarithmic scale for both the x-axis and y-axis. Analyze the convergence behavior based on the slope of these curves.**(d)** For the root with linear convergence observed in part (c), repeat the analysis using the secant method.

The given function is f(x)=54x6+45x5−102x4−69x3+35x2+16x−4Newton's method is a numerical method of…

Set f(x) = 54x6 + 45x5 — 102x4 – 69x³ +35x² + 16x – 4. (b) Use Newton's Method to find all five roots in the interval (correct to eight decimal places). (c) For each root, use the value obtained in part (b) to approximate its exact value |- r| denote the (absolute) error at step i in Part (b). Plot the curve (ei, ei+1). Please use logarithm scale for both the x-axis and y-axis. What can we say about the convergence based on the slope of these curves. (d) For the one with linear convergence, redo part (c) using secant method. =

Set f(x) = 54x6 + 45x5 — 102x4 – 69x³ +35x² + 16x – 4. (b) Use Newton's Method to find all five roots in the interval (correct to eight decimal places). (c) For each root, use the value obtained in part (b) to approximate its exact value |- r| denote the (absolute) error at step i in Part (b). Plot the curve (ei, ei+1). Please use logarithm scale for both the x-axis and y-axis. What can we say about the convergence based on the slope of these curves. (d) For the one with linear convergence, redo part (c) using secant method. =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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